Typing environment

In type theory a typing environment (or typing context) represents the association between variable names and data types.

More formally an environment $\Gamma$ is a set or ordered list of pairs $\langle x,\tau \rangle$, usually written as $x:\tau$, where $x$ is a variable and $\tau$ its type.

The judgement

$\Gamma \vdash e:\tau$

is read as "$e$ has type $\tau$ in context $\Gamma$".

In statically typed programming languages these environments are used and maintained by type rules to type check a given program or expression.

See also

• Type system
• Type rule
• Type theory